SOLUTION: Demand Suppose that the demand D for candy at the movie theater is inversely related to the price p. (a) When the price of candy is $2.75 per bag, the theater sells 156 bags of

Algebra ->  Equations -> SOLUTION: Demand Suppose that the demand D for candy at the movie theater is inversely related to the price p. (a) When the price of candy is $2.75 per bag, the theater sells 156 bags of      Log On


   

Question 1208016: Demand Suppose that the demand D for candy at the movie theater is inversely related to the price p.
(a) When the price of candy is $2.75 per bag, the theater sells 156 bags of candy.Express the demand for candy in terms of its price.

(b) Determine the number of bags of candy that will be sold if the price is raised to $3 a bag.
Found 3 solutions by josgarithmetic, timofer, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
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Enough of these. The written language description works the same as it always does.



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Read the first sentence description very carefully. You are making a mistake by maybe reading too fast and misreading.

Answer by timofer(104) About Me  (Show Source):
You can put this solution on YOUR website!
Variation description with D for demand and p for price

The first sentence says D=k%2Fp.
The factor k is needed because, "related to the ", as in D is related to p. In this case, "inversely".


part (a)
p is 2.75 and D is 156 bags of candy.
156=k%2F2.75
k=2.75%2B156
k=429

You have equation D=429%2Fp


You should be able to figure out part (b).

Answer by greenestamps(13198) About Me  (Show Source):
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The way the problem is presented, you are probably expected to use the equation from part (a) to answer part (b).

However, the actual computation for inverse variation is easier if you simply use the fact that the product of the price and the number of bags is constant.

So, in this example....

2.75(156) = 3.00(x)
x = 2.75(156)/3 = 2.75(52) = 104+39 = 143

ANSWER: 143 bags

A different easy way to do the computation is to use the fact that the ratio of numbers of bags is the reciprocal (inverse) of the ratio of prices.

The price changes by a factor of 3.00/2.75 = 12/11; the number of bags must change by a factor of 11/12:

156(11/12) = 11(13) = 143